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Harold R. (Hal)
Foster’s Prince Valiant
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“In mathematics, the greatest degree of self-evidence is usually not to be found quite at the beginning, but at some later point; Hence the early deductions, until they reach this point, give reasons rather for believing the premises because true consequences follow from them, than for believing the consequences because they follow from the premises.”
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Dan DeCarlo The
greatest of all time comic book artist!
Archie Andrews
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Harold R. (Hal)
Foster’s Prince Valiant
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Artists unknown © Respective
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Pencils: Stan Goldberg Inks: Jon D'Agostino Josie Gang
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Personally I approach
this work with great confidence, and so very much of its apparent complexity melts
away. The oppressive notations that the authors felt that (rightly) it was necessary
to include in order hold the attention of conventional mathematicians, skeptical,
at best, of this, then very modern work. By laying their proofs with each
proceeding proposition and the extensive demonstrations of certain further proofs.
By now we should be well able to read these equations and discern at least some
varying meaning from them. Just to repeat the key to opening up an
understanding to this section, all propositions are to be numbers which are all
either 1 or 0.
Treated as a "calculus," the rules of deduction are capable of many other interpretations. But all other interpretations depend upon the one here considered, since in all of them we deduce consequences from our rules, and thus presuppose the theory of deduction. One very simple interpretation of the "calculus " is as follows: The entities considered are to be numbers which are all either 0 or 1; "p:) q" is to have the value 0 if p is 1 and q is 0; otherwise it is to have the value 1;, p is to be 1 if p is 0, and 0 if p is 1; p. q is to be 1 if p and q are both 1, and is to be 0 in any other case; p v q is to be 0 if p and q are both 0, and is to be 1 in any other case; and the assertion-sign is to mean that what follows has the value 1. Symbolic logic considered as a calculus has undoubtedly much interest on its own account; but in our opinion this aspect has hitherto been too much emphasized, at the expense of the aspect in which symbolic logic is merely the most elementary part of mathematics, and the logical prerequisite of all the rest. For this reason, we shall only deal briefly with what is required for the algebra of symbolic logic.
I can’t help wondering if Whitehead and Russell may have
erred in dismissing the binary calculus that runs our computers today. It seems
to be right on the tip of their tongues. Still they clearly had other fish to
fry, and this work certainly demanded a focused attention.
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Harold R. (Hal)
Foster’s Prince Valiant
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